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Some subclasses of Petri nets and the analysis of their structural properties: a new approach

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4 Author(s)
Amer-Yahia, C. ; Lab. de Comception e Conduite des Syst., Univ. de Tizi-Ouzou, Algeria ; Zerhouni, N. ; Moudni, A.E. ; Ferney, M.

The purpose of the paper is to consider some special types of Petri nets, introduced by Lien (1976), and to propose a complete and unified approach for the study of their structural properties by using techniques of linear algebra of matrices. We distinguish four subclasses: forward-conflict-free, backward-conflict-free, forward-concurrent-free, and backward-concurrent-free Petri nets. A modification of the classical incidence matrix results in a square matrix, called a modified incidence matrix, with nonpositive (nonnegative) off-diagonal elements when backward-(forward-) conflict-free or concurrent-free Petri nets are considered. The modified incidence matrix eigenvalues are computed and theorems on matrices of this type are used to prove several sufficient and/or necessary conditions for structural boundedness, liveness, repetitiveness, conservativeness, and consistency of these four subclasses of Petri nets

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Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on  (Volume:29 ,  Issue: 2 )